Faraday's Law and magnetic field

A coil containing N = 550 turns with radius r = 3.90 cm, is placed in a uniform magnetic field that varies with time according to [tex]B=(At + Bt^4)[/tex], where [tex]A = 1.05 \cdot 10^−2 {\rm T}/{\rm s}[/tex] and [tex]B = 3.00 \cdot 10^−5 {\rm T}/{\rm s}^{4}[/tex]. The coil is connected to a resistor of resistance 640 Ohms, and its plane is perpendicular to the magnetic field. The resistance of the coil can be neglected.

Find the magnitude of the induced emf in the coil as a function of time. Write your answer as an expression in terms of the variables given in the problem.

I'm thinking that the derivative of magnetic flux can be written as the derivative of (BA). A is constant, so it's A multiplied by the derivative of B.